To the question of the integration of Plebansky Equation

TL;DR

The paper demonstrates that the Plebansky equation's symmetries have an infinite set of explicit solutions, enabling the derivation of series solutions and presenting specific classes of explicit solutions.

Contribution

It introduces explicit solutions for the Plebansky equation's symmetries and shows the potential for series solutions in analytic form.

Findings

Infinite set of symmetry solutions for Plebansky equation

Explicit classes of solutions provided

Potential for series solutions in analytic form

Abstract

It is shown that corresponding to Plebansky equation of symmetry posses the infinite set of solutions, which we present in explicit form. This fact leads to conclusion about possibility to find series solutions of the Plebansky equation in analytic form. Some classes of explicit solution are presented.